Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T09:21:15.190Z Has data issue: false hasContentIssue false
  • English
  • Français

A Remark on Configuration Spaces of Two Points

Part of: Topological manifolds Fiber spaces and bundles

Published online by Cambridge University Press:  11 April 2018

George Raptis  and
Paolo Salvatore
George Raptis
Affiliation:
Universität Regensburg, Fakultät für Mathematik, 93040 Regensburg, Germany
Paolo Salvatore*
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy ([email protected])
*
*Corresponding author.
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove a homotopy invariance result for a certain covering space of the space of ordered configurations of two points in M × X where M is a closed smooth manifold and X is any fixed aspherical space which is not a point.

Keywords

configuration spacehomotopy invariancespherical tangent bundle

MSC classification

Primary: 55R80: Discriminantal varieties, configuration spaces
Secondary: 57N65: Algebraic topology of manifolds
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 2 , May 2018 , pp. 599 - 605
Copyright
Copyright © Edinburgh Mathematical Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Benlian, R. and Wagoner, J., Type d'homotopie fibré et réduction structurale des fibrés vectoriels, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A207–A209.Google Scholar
2.Boardman, J. M. and Vogt, R. M., Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Volume 347 (Springer-Verlag, Berlin–New York, 1973).Google Scholar
3.Dugger, D. and Isaksen, D. C., Topological hypercovers and 𝔸1-realizations, Math. Z. 246(4) (2004), 667–689.CrossRefGoogle Scholar
4.Dupont, J. L., On homotopy invariance of the tangent bundle. I, II, Math. Scand. 26 (1970), 5–13; ibid. 26 (1970), 200–220.Google Scholar
5.Evans-Lee, K., On configuration spaces of lens spaces, PhD thesis, University of Miami (2015).Google Scholar
6.Kwasik, S. and Rosicki, W., On stability of 3-manifolds, Fund. Math. 182(2) (2004), 169–180.Google Scholar
7.Levitt, N., Spaces of arcs and configuration spaces of manifolds, Topology 34(1) (1995), 217–230.Google Scholar
8.Longoni, R. and P. Salvatore, Configuration spaces are not homotopy invariant, Topology 44(2) (2005), 375–380.Google Scholar